Observation of edge magnetoplasmons (EMP) was one of the most unexpected discoveries in physics of two-dimensional electron systems (2DES). In contrast to 'bulk' 2DES plasmons with frequencies equal to or larger than the cyclotron frequency, the edge magnetoplasmons confine near the edge of 2DES and have a gapless spectrum. The possibility of observing EMP in different kinds of 2DES realised in the semiconductor structure, on the liquid helium surface or in 2D sheet of ions trapped below the helium surface offers a powerful spectroscopic tool for the study of the general properties of 2DES. The main purpose of this book is to outline theoretical concepts and some recently obtained results of experimental investigations of EMP in 2DES. The theories presented in this book cover a broad range of intensively studying EMP properties, while the experimental part of the book is mainly focused on just a few intriguing results. In addition, attention is paid to the possible EMP applications.